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Standard X

Mathematics

Ratio of Area of Two Triangles Having Same Height

In triangle A...

Question

In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then which of the following conditions is/are true?

AE = AD

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$D E ∥ B C$

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$∠ A D E = ∠ A C B$

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DE = BD

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Solution

The correct option is B
$D E ∥ B C$

$Given : A B = 18 c m, A D = 8 c m, A E = 12 c m and E C = 15 c m$

$∴ D B = A B - A D = 18 - 8 = 10 cm$

$Now, \frac{A D}{D B} = \frac{8}{10} = \frac{4}{5}$

$and \frac{A E}{E C} = \frac{12}{15} = \frac{4}{5}$

$∵ \frac{A D}{D B} = \frac{A E}{E C}$

$∴ D E ∥ B C (By converse of basic proportionality theorem)$

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Similar questions

In a $Δ A B C$ , D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC:
(i) AB = 12cm, AD = 8 cm, AE = 12 cm and AC= 18cm.
(ii)AB = 5.6cm, AD= 1.4cm, AC = 7.2 cm and AE= 1.8 cm.
(iii) AB= 10.8 cm, BD= 4.5cm, AC = 4.8cm and AE =2.8 cm.
(iv)AD = 5.7cm, BD = 9.5cm, AE = 3.3cm and EC = 5.5 cm.

D and E are points on the sides AB and AC respectively of a $Δ A B C$ . In each of the follwing cases, determine whether DE || BC or not.

(i) AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

(ii) AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm.

(iii) AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

(iv) AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.

Q. D and E are points on the sides AB and AC respectively of a

∆ A B C

. In each of the following cases, determine whether

D E ∥ B C

or not.

(i)

A D = 5.7 cm, D B = 9.5 cm, B D = 4.8 cm and E C = 8 cm .

(ii)

A B = 11.7 cm, A C = 11.2 cm, B D = 6.5 cm and A E = 4.2 cm .

(iii)

A B = 10.8 cm, A D = 6.3 cm, A C = 9.6 cm and E C = 4 cm .

(iv)

A D = 7.2 cm, A E = 6.4 cm, A B = 12 cm and A C = 10 cm .

Q. In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then which of the following conditions is/are true?

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In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then which of the following conditions is/are true?

The correct option is B DE∥BC Given : AB=18 cm,AD=8 cm,AE=12 cm and EC=15 cm ∴DB=AB−AD=18−8=10 cm Now, ADDB=810 = 45 and AEEC=1215=45 ∵ADDB = AEEC ∴DE∥BC (By converse of basic proportionality theorem)